Answer:
The asymptotes are the x-values for which the tangent function is not defined. We draw these in to remind us that the function does not cross that line. They are the odd multiples of 90°
see the attachments below for the steps :)
The simplified expression is as follows:
d(-3x^2 + 9x - 14)
Step-by-step explanation:
so, we need to find the smallest common multiple of 36 and 42.
that is the smallest number I can divide both by 36 and 42 without remain.
let's use the method of basic prime factors (we start with the smallest fitting prime number - 2 is a prime number too - and divide as often as possible, then continue with the next bigger prime number, until there is nothing left to divide) :
36 / 2 = 18
18 / 2 = 9
9 / 3 = 3
3 / 3 = 1 finished
therefore,
36 = 2×2×3×3
42 / 2 = 21
21 / 3 = 7
7 / 5 does not work
7 / 7 = 1 finished
therefore,
42 = 2×3×7
to find the smallest common multiple (SCM) we check the maximum length of each prime factor sequence.
and we see 2 times 2, 2 times 3 and 1 time 7.
so, the SCM = 2×2×3×3×7 = 252.
there is no smaller number that can be divided by both 36 and 42 without remain.
so, the rod must be at least 252 cm long to cut it into equally long pieces of either 36 cm (7 pieces) or 42 cm (6 pieces).
Steps to Calculate Hours
3ℎ+18×1ℎ60+0×1ℎ3600
3
h
r
+
18
m
i
n
×
1
h
r
60
m
i
n
+
0
s
×
1
h
r
3600
s
=3ℎ+0.3ℎ+0ℎ
=
3
h
r
+
0.3
h
r
+
0
h
r
=3.3ℎ
Steps to Calculate Minutes
3ℎ×601ℎ+18+0×160
3
h
r
×
60
m
i
n
1
h
r
+
18
m
i
n
+
0
s
×
1
m
i
n
60
s
=180+18+0
=
180
m
i
n
+
18
m
i
n
+
0
m
i
n
=198
=
198
m
i
n
Steps to Calculate Seconds
3ℎ×36001ℎ+18×601+0
3
h
r
×
3600
s
1
h
r
+
18
m
i
n
×
60
s
1
m
i
n
+
0
s
=10800+1080+0
=
10800
s
+
1080
s
+
0
s
=11880
=
11880
s
hope this helps
3^y, x&y both have to be greater than 0 in which case the greater number will have the greatest value , since y >x . 3^y > 3^x
